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In this article, frequency analysis of multi-sized hybrid nano-composites (MHC) disk (MHCD) resting on elastic media and located in an environment with gradually changed temperature feature is presented. Carbon fibers (CF) or carbon nanotubes (CNTs) in the macro or nano sizes respectively are responsible for reinforcing the matrix. For prediction of the efficiency of the properties MHCD's modified Halpin-Tsai theory has been presented. The strain-displacement relation in multi-sized laminated disk's dynamics through applying third-order-shear-deformation-theory is determined. The energy methods called Hamilton's principle is applied for deriving the motion equations along with boundary conditions, which has ultimately been solved using generalized differential quadrature method. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. At the final stage, the outcomes illustrate that patterns of FG, fibers' various directions, the WCNT and VF factors, top surface's applied temperature have considerable impact on the MHCD's dynamics. Another important consequence is that MHC structure with FG-A and UD patterns have a similar effect on the dimensionless natural frequency of the GPLRC disk, while FG-X has the lowest stability and natural frequency. A useful suggestion is that increasing the value of the length to thickness ratio of MHC not only decreases the central deflection of the structure through time but also causes to decrease real-time domain changes for the MHC viscoelastic annular plate. Numerical results declare that viscoelastic disks fabricated from the hybrid nanocomposites can endure higher frequencies compared with those consisted of conventional composites. [ABSTRACT FROM AUTHOR]